Reciprocals, Powers of 10, and Euler's Totient Function - Math Foundations 202

Explore the fascinating connections between decimal expansions of fractions, modular arithmetic, and Euler's totient function in this 24-minute mathematics lecture. Delve into the intricacies of repeated decimal cycles in fractions, examining their length and patterns. Discover how these concepts relate to powers of 10 in modular arithmetic and the role of Euler's phi function in extending Fermat's theorem. Gain valuable insights into this interconnected circle of mathematical ideas, enhancing your understanding of number theory and algebraic structures.